I would crack down on some of it, and let other stuff go.
What I'd crack down on is:
1) We don't throw out perfectly good stuff. Nothing goes in the garbage unless it's beyond repair. Things need to be cleaned, sorted, folded, grouped with like objects (all Legos together, all clothes organized and socks matched, doll clothes packed separately) and so on. Take her to the local liquor store where they always have tons of free boxes at the exit - some even have dividers which can be useful in protecting things that shouldn't just be thrown in a heap. SHE can give up screen time to sort and package and label on the outside of the box. You can sit there with a book or a glass of wine to supervise.
2) Let her know that things will not be replaced unless she has outgrown them.
3) Let her know that you are not her slave. It's not up to you to sort or to give up your family values of not tossing things.
4) YOU are not doing her laundry at her direction. In fact, you're not doing ANYTHING "when she tells you to." She's now in charge of it so it's totally within her control. Buy her whatever laundry basket she needs (apparently a tiny one) and put it on the floor of her closet. Her stuff goes in there. Give her one laundry lesson (water level, temp, soap amount, etc.) and post an instruction sheet above the washer. Walk away.
5) You will not listen to any complaining when she doesn't have clean clothes or when her friends criticize her for wearing the same things twice in a week. (Not that they should criticize her, of course - you can suggest that she tell them she's not interested in possessions.)
6) When you locate some worthy organizations for donations, have HER put the boxes in the car and go with you to haul them into the charity's office. I think it's okay to go with her and help her speak to the receptionist or donations coordinator to say these are things she no longer wants and you both just know there are plenty of needy and grateful kids who would love them. For example, I have given to a Latino service agency and a battered women's shelter thrift shop - both service people who have left their homes with nothing but the shirts on their backs. Sobering. And let the agency tell your daughter how appreciative others will be! (You can call ahead to give them a head's up as long as they don't think you're asking them to do your job for you.)
What I'd give up on is:
1) forcing her to wear socks.
2) forcing her to wear a dress to church. Be grateful that she goes. If you're in a church that is strict about that, reassess how important it is.
3) Don't even force her to keep the American Girl dolls. 11 year olds often aren't interested in dolls, and too many young kids get their relatives to spend a fortune on these things more because everyone's talking about it and not because they really enjoy them. I hated dolls as a kid, never owned a Barbie, etc.
What I'd keep are a box of things like Grandma's gift from her travels and anything else that's sentimental. I'm not sure what the statue or music box are, but you'll know whether those are valuable. I'd have her pack it all in a box and label it (family things or sentimental things) and act like it goes to a unique charity, and then just put it in the attic or on your bedroom closet shelf so she doesn't see it and know you kept it. That stuff is not replaceable, and if she does have a bout of regret, at least there's a chance to restore it.
I'd consider putting some things on Craig's List or other site, and taking some things to a children's resale shop. Any money you make can go into a college fund, or perhaps a "Remorse Fund" to buy things at a thrift shop to replace things when she comes to her senses. You can let her spend the money until it runs out. Otherwise she's out of luck. Or, if she wants to hold a big yard sale for HER stuff (and get up at 6 AM and do all the work), she can keep the cash.
And I'd be sure to NOT have nearly as much time for her whims since you now have to sort/donate/drive/list things on line etc. So, gee, you don't have time to take her to the mall or plan a sleepover or buy her favorite snacks. In fact, it wouldn't hurt for you to forget to pay her on-line bill giving her internet access for her iPad. You can also be short of cash to pay her field trip fee or buy her XYZ because you spent it on gas to go collect boxes and drive to charities and donation centers.
At this age, it's really helpful to NOT yell or lecture (no matter how much they deserve it), and just lay out the consequences. Then, anything unpleasant that happens later (no clothes, no toys, no iPad...) is HER choice and HER decision. If she's crying or upset, your answer is a calm, emotionless, "How unfortunate for you. I have plenty of clothes (or clean laundry or books...fill in the blank) because I appreciate and take care of my things."
If she doesn't want to do all the work, then she can put the trash bags back in her room, but they aren't staying in the hall.
The only thing you have to look at is your statement that you are fed up and she is ungrateful. This didn't happen overnight. How did she get this way, and what have you allowed that perhaps contributed to creating this monster? (And I'm not being critical - we ALL do something we shouldn't have, we all allow things we maybe look back and wish we hadn't.) But if you allowed her to gradually get into iPad addiction, accept your role in that and tell her you were too lenient. But you can certainly disable some games if she needs the time to sort/clean/donate or do laundry. As long as it's more work for her to do the throwing out, she'll have to really evaluate her choices.
I suspect she will come around sooner or later and regret her attitude. By all means, make her WORK for the money for new clothes, say "no" to high end brand names, and so on.
And finally, make sure this is not the sign of depression and "I hate everything" that needs intervention. I assume you monitor her iPad usage and she's not on line without your knowledge. I'm not an iPad expert by any means, but I understand there are all kinds of hidden apps that kids learn early on to "hide" behind a simple calculator or other innocuous looking app. If you are close to her friends' parents, you can discreetly inquire about whether they are going through this as well.
Good luck!